derivative of x^3(x^4-1)

Lösung

\frac{d}{d x} (x^{3} (x^{4} - 1))

7 x^{6} - 3 x^{2}

Schritte zur Lösung

\frac{d}{d x} (x^{3} (x^{4} - 1))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = x^{4} - 1

= \frac{d}{d x} (x^{3}) (x^{4} - 1) + \frac{d}{d x} (x^{4} - 1) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (x^{4} - 1) = 4 x^{3}

= 3 x^{2} (x^{4} - 1) + 4 x^{3} x^{3}

Vereinfache

3 x^{2} (x^{4} - 1) + 4 x^{3} x^{3} : 7 x^{6} - 3 x^{2}

= 7 x^{6} - 3 x^{2}

t an g e n t f (x) = - 3 x^{3} - 2 x^{2} - 1, at - 1

in v erse l a pl a ce \frac{s + 3}{s + 1 ( s + 2 )}

\int - 2 sin^{2} (t) d t

\frac{\partial}{\partial x} (4374 x^{\frac{1}{3}} + 2 y)

x \to 1 lim (\frac{e ^{x} - 1}{x})